Editing Compressed Sensing Tomography (section)

==Further Information==

* [[Direct Fidelity Estimation]] can be further generalised to work with low-rank states. Thus, one can use compressed sensing tomography to get an estimated density matrix and use Direct fidelity estimation to check whether this state agrees with the true state. This check is guaranteed to be sound, even if the true state is not approximately low rank. Hence this is used to certify the state.
* Compressed sensing tomography (as mentioned in [https://arxiv.org/abs/1205.2300 Steven T. Flammia et al]) can also be applied to Quantum Process tomography. This method would have an advantage when the unknown quantum process has a small Kraus rank (only be expressed with a few Kraus operators). This occurs, for example, when the unknown process consists of unitary evolution combined with local noise (acting on each qubit individually, or acting on small subsets of the qubits). The process here can be characterised in <math>m = O(rd^2 </math>log<math> d)</math> settings